## CHAPTER 1 BASIC HOMEWORK

### Multiplication by One

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**Question 1**

If a ratio is equivalent to one, so is its inverse. When multiplying by one use the ratio which correctly cancels units. Convert 51 cm to inches. (1 in = 2.54 cm) **U**se 3 sig. fig. for this problem.

First, study the following examples,

**Explanation**

**Explanation**

Dimensional Analysis will actually save your life and grades so be sure to completely understand this topic! 51 cm x 1 in / 2.54 cm = 20.1 in

**Question 2**

Convert 848 nm to m. (1 nm = 10-9m)

(Use 3 significant figures. For scientific notation, 2,340 is inputted as 2.34e3 and 6.04×10-5 is inputed as 6.04e-5.)

**Explanation**

**Explanation**

848 nm x 1 m/ 10^-9 nm = 8.48e^-7 m

**Question 3**

Convert 28.4 rods to ft. (1 rod = 16.5 ft)

**Explanation**

**Explanation**

28.4 rods * 16.5 ft / 1 rod = 469 ft

**Question 4**

How many mph (mi/hr) is 56.2 ft/sec?

**Explanation**

**Explanation**

38.3 mi/ hr * 3600 hr/sec * 5280 ft/mi = 38.3 ft/sec

**Question 5**

Convert 1 m to feet. Hint: use the following path m –> cm –> in –> ft

**Explanation**

**Explanation**

1 m * 100 cm/ 1 m * 1 in/2.54 cm * 1 ft/ 12 in = 3.28 ft

**Question 6**

How many in3 are 469 cm3? (2.54 cm = 1 in.) Hint given in feedback.

**Explanation**

**Explanation**

Hints: (1 in)3 = (2.54 cm)3 469 cm3 * 13 in3/ 2.543 cm3 = 28.6 in3

**Question 7**

How many pounds does 31.8 in3 of gold weigh? (The density of gold is 19.3 g/cm3, 2.54 cm = 1 in, and 454 g = 1 lb.) Hint given in feedback. Note these are not large volumes–a cup of water is about 30 in3.

**Explanation**

**Explanation**

Hints: (1 in)3 = (2.54 cm)3 Path: in3 –> cm3 –> g –> lbs 31.8 in3 *(2.54 cm)3/ (1 in)3 * 19.3 g /1 cm3* 1 lb/ 454 g = 22.2 lb